Networks of Common Asset Holdings : Aggregation and Measures of Vulnerability Andreea Minca Cornell University, Operations Research Department Joint work with : Anton Braverman, Cornell University Apr 8 2014 ECB Workshop on Using Big Data for Forecasting and Statistics Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 1 / 14
Introduction : Financial linkages Financial networks have been used to model the propagation of distress due to insolvency. It is now believed that the most important sources of financial distress come from illiquidity and price mediated contagion effects. Linkages that transmit price feedback effects : not direct claims but overlap in portfolio holdings. Since they are not direct claims, they are not directly observable form data. Research question : How to measure the linkages due to common assets? Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 2 / 14
Model Network model N = {1,...,N} is a set of portfolios K = {1,...,K } is a set of stocks S = (s 1,...,s K ) is a vector of stock prices B = [β ki ] i N,k K the holdings matrix : β ki represents the number of shares of stock k owned by portfolio i. The value of portfolio i can be written as P i = K k=1 β ki s k = β i S, where β i = (β 1i,...,β Ki ). Network model : portfolios (funds) represent nodes. The strength of the links (edge weights) between any two portfolios are defined by answering the following question : what effect will the liquidation of fund i have on fund j? Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 3 / 14
Model The weight of an edge between two portfolios is model based : what effect will the liquidation of fund i have on fund j? Initial shock : Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 4 / 14
Model The weight of an edge between two portfolios is model based : what effect will the liquidation of fund i have on fund j? Initial shock : Uniform redemptions / forecast of redemptions / contemporaneous redemptions ; Behavior of a fund : Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 4 / 14
Model The weight of an edge between two portfolios is model based : what effect will the liquidation of fund i have on fund j? Initial shock : Uniform redemptions / forecast of redemptions / contemporaneous redemptions ; Behavior of a fund : Assumption : proportional liquidation ; Impact on other funds : Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 4 / 14
Model The weight of an edge between two portfolios is model based : what effect will the liquidation of fund i have on fund j? Initial shock : Uniform redemptions / forecast of redemptions / contemporaneous redemptions ; Behavior of a fund : Assumption : proportional liquidation ; Impact on other funds : Need to model the liquidity of each stock and define the edge weights ; Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 4 / 14
Model Edge weights under linear price impact The price impact function is linear and of the form : PI k (x) = x λ k, where λ k is such that buying/selling λ k stocks will move the price of the asset 100 up/down by 1%. The parameter λ k captures the market depth of stock k (Kyle 85), with λ k = 1 λ ADV k, σ k where ADV k is the average daily volume of trades, σ k is the daily returns standard deviation of stock k and λ is an invariant across stocks (Kyle & Obizaheva 2011) Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 5 / 14
Model When portfolio i liquidates its shares of asset k, the price of the asset s k drops by β ki λ k s k. The value of portfolio j decreases by β kj β ki λ k s k. The total loss experienced by j if portfolio i liquidates defines the edge weight w ij = K k=1 β ki λ k β kj s k. Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 6 / 14
Data Data Quarterly mutual fund holdings data from the CRSP Mutual Fund database ranging from 01/2003-12/2012. We use only US equity funds and portfolios with TNA above 100 millions. Fund flows are calculated using Flow t = TNA t (1 + r t )TNA t 1 TNA t 1, where TNA t is the total net assets of a portfolio in period t and r t is the return of the portfolio in period t. To calculate stock market depths we use daily stock data from the CRSP US Stock Database. Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 7 / 14
Data vulnerability measure We define the Vulnerability measure as the cumulative first order effects on node i s loss that are imposed by its neighbors : VI i = 1 N P i w ji. j=1 j i Interpretation : εvi i represents the fraction by which portfolio i s value will decrease (increase) if all its neighbors liquidate (expand) their portfolios by a factor of ε. Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 8 / 14
Data The most significant drops in cumulative TNA occured in Q4 2008, shortly after the collapse of the Lehman Brothers, and in Q3 2011 during which S&P downgraded the U.S. credit rating. TABLE: Fund returns during quarter t regressed against fund vulnerability at the start of the quarter. 2008Q4 2011Q3 Constant -0.2117-0.1239 (-58.56) (-47.26) VI t -0.0270-0.0801 (-7.14) (-20.57) Adj. R 2 0.0179 0.1012 Observations 2748 3749 t statistics in parentheses p < 0.05, p < 0.01, p < 0.001 Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 9 / 14
Data FIGURE: Average portfolio vulnerability VI plotted alongside the cumulative TNA of all portfolios. Data for 09/2010 is missing. This suggests that increases in average vulnerability precede significant drops in total net assets. Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 10 / 14
Data Two refinements F i : the flow to be experienced by fund i over the current quarter. 1 The flow-adjusted vulnerability (FAV) measure for fund i FAV i = 1 P i N j=1f j w ji, 2 The measure of vulnerability to order imbalance. (( ) α FAV i = 1 K ˆNB,k P i β ki s k 1). k=1 ˆN S,k where for stock k, we set the estimators for the number of buyers/sellers ˆN B,k = ˆN S,k = N i=1 N i=1 β ki F i 1 {Fi >0}, β ki F i 1 {Fi <0}. Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 11 / 14
Results Results TABLE: Fama-Macbeth regressions of future fund returns with Newey-West corrections of four lags. The dependent variable is fund return over quarter t, the FAV and FAV measures are computed using the asset holdings at the start of quarter t and the fund flows over quarter t. (1) (2) (3) FAV t 0.0683 0.0705 (4.85) (4.36) FAV t 0.463-0.00706 (4.38) (-0.08) log(tna t 1 ) 0.00101 0.000635 0.000623 (0.69) (0.41) (0.39) log(shares t 1 ) -0.000800-0.000352-0.000333 (-0.57) (-0.24) (-0.22) Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 12 / 14
Results (1) (2) (3) flow t 0.0230 0.0162 0.0155 (4.55) (3.49) (3.34) return t 1 0.000742-0.0233-0.0251 (0.02) (-0.51) (-0.56) Constant 0.0227 0.0205 0.0203 (1.48) (1.29) (1.23) Sample Size 87257 87257 87257 R 2 0.1746 0.2032 0.2105 t statistics in parentheses p < 0.05, p < 0.01, p < 0.001 Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 13 / 14
Conclusions Conclusions The network representation allows us to derive measures of vulnerability of funds to the shocks held by their neighbors in the network. We find, using mutual fund data, that the vulnerability index is useful in predicting returns in periods of mass liquidations. In such periods, we can identify vulnerable funds based on asset holdings and the liquidity characteristics of the stocks. The flow-adjusted measure of vulnerability to order imbalance, based on our model for the price impact of trading, is shown to be correlated with returns throughout all our sample period, not only during periods of mass liquidations. Andreea Minca (Cornell University) Networks of Common Asset Holdings Apr 8 2014 14 / 14